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88
Krylov Projection Methods For Model Reduction
, 1997
"... This dissertation focuses on efficiently forming reducedorder models for large, linear dynamic systems. Projections onto unions of Krylov subspaces lead to a class of reducedorder models known as rational interpolants. The cornerstone of this dissertation is a collection of theory relating Krylov p ..."
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Cited by 118 (3 self)
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This dissertation focuses on efficiently forming reducedorder models for large, linear dynamic systems. Projections onto unions of Krylov subspaces lead to a class of reducedorder models known as rational interpolants. The cornerstone of this dissertation is a collection of theory relating Krylov projection to rational interpolation. Based on this theoretical framework, three algorithms for model reduction are proposed. The first algorithm, dual rational Arnoldi, is a numerically reliable approach involving orthogonal projection matrices. The second, rational Lanczos, is an efficient generalization of existing Lanczosbased methods. The third, rational power Krylov, avoids orthogonalization and is suited for parallel or approximate computations. The performance of the three algorithms is compared via a combination of theory and examples. Independent of the precise algorithm, a host of supporting tools are also developed to form a complete modelreduction package. Techniques for choosing the matching frequencies, estimating the modeling error, insuring the model's stability, treating multipleinput multipleoutput systems, implementing parallelism, and avoiding a need for exact factors of large matrix pencils are all examined to various degrees.
Reducedorder modeling of large linear subcircuits via a block Lanczos algorithm
 In Proc. 32nd ACM/IEEE Design Automation Conf
, 1995
"... A method for the e�cient computation of accu� rate reduced�order models of large linear circuits is de� scribed. The method � called MPVL � employs a novel block Lanczos algorithm to compute matrix Pad�e ap� proximations of matrix�valued network transfer func� tions. The reduced�order models � compu ..."
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Cited by 67 (21 self)
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A method for the e�cient computation of accu� rate reduced�order models of large linear circuits is de� scribed. The method � called MPVL � employs a novel block Lanczos algorithm to compute matrix Pad�e ap� proximations of matrix�valued network transfer func� tions. The reduced�order models � computed to the re� quired level of accuracy � are used tospeed up the anal� ysis of circuits containing large linear blocks. The lin� ear blocks are replaced by their reduced�order models� and the resulting smaller circuit can be analyzed with general�purpose simulators � with signi�cant savings in simulation time and � practically � no loss of accuracy. 1
ReducedOrder Modeling Techniques Based on Krylov Subspaces and Their Use in Circuit Simulation
 Applied and Computational Control, Signals, and Circuits
, 1998
"... In recent years, reducedorder modeling techniques based on Krylovsubspace iterations, especially the Lanczos algorithm and the Arnoldi process, have become popular tools to tackle the largescale timeinvariant linear dynamical systems that arise in the simulation of electronic circuits. This pape ..."
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Cited by 53 (10 self)
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In recent years, reducedorder modeling techniques based on Krylovsubspace iterations, especially the Lanczos algorithm and the Arnoldi process, have become popular tools to tackle the largescale timeinvariant linear dynamical systems that arise in the simulation of electronic circuits. This paper reviews the main ideas of reducedorder modeling techniques based on Krylov subspaces and describes the use of reducedorder modeling in circuit simulation. 1 Introduction Krylovsubspace methods, most notably the Lanczos algorithm [81, 82] and the Arnoldi process [5], have long been recognized as powerful tools for largescale matrix computations. Matrices that occur in largescale computations usually have some special structures that allow to compute matrixvector products with such a matrix (or its transpose) much more efficiently than for a dense, unstructured matrix. The most common structure is sparsity, i.e., only few of the matrix entries are nonzero. Computing a matrixvector pr...
Krylov Subspace Techniques for ReducedOrder Modeling of Nonlinear Dynamical Systems
 Appl. Numer. Math
, 2002
"... Means of applying Krylov subspace techniques for adaptively extracting accurate reducedorder models of largescale nonlinear dynamical systems is a relatively open problem. There has been much current interest in developing such techniques. We focus on a bilinearization method, which extends Kry ..."
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Cited by 50 (3 self)
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Means of applying Krylov subspace techniques for adaptively extracting accurate reducedorder models of largescale nonlinear dynamical systems is a relatively open problem. There has been much current interest in developing such techniques. We focus on a bilinearization method, which extends Krylov subspace techniques for linear systems. In this approach, the nonlinear system is first approximated by a bilinear system through Carleman bilinearization. Then a reducedorder bilinear system is constructed in such a way that it matches certain number of multimoments corresponding to the first few kernels of the VolterraWiener representation of the bilinear system. It is shown that the twosided Krylov subspace technique matches significant more number of multimoments than the corresponding oneside technique.
KrylovSubspace Methods for ReducedOrder Modeling in Circuit Simulation
 J. Comput. Appl. Math
, 1999
"... The simulation of electronic circuits involves the numerical solution of very largescale, sparse, in general nonlinear, systems of differentialalgebraic equations. Often, the size of these systems can be reduced considerably by replacing the equations corresponding to linear subcircuits by approxim ..."
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Cited by 43 (9 self)
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The simulation of electronic circuits involves the numerical solution of very largescale, sparse, in general nonlinear, systems of differentialalgebraic equations. Often, the size of these systems can be reduced considerably by replacing the equations corresponding to linear subcircuits by approximate models of much smaller statespace dimension. In this paper, we describe the use of Krylovsubspace methods for generating such reducedorder models of linear subcircuits. Particular emphasis is on reducedorder modeling techniques that preserve the passivity of linear RLC subcircuits. Key words: Lanczos algorithm; Arnoldi process; Linear dynamical system; VLSI interconnect; Transfer function; Pad'e approximation; Stability; Passivity; Positive real function 1 Introduction Today's integrated electronic circuits are extremely complex, with up to tens of millions of devices. Prototyping of such circuits is no longer possible, and instead, computational methods are used to simulate and ...
ReducedOrder modeling of large passive linear circuits by means of the SyPVL algorithm
 in Tech. Dig. 1996 IEEE/ACM International Conference on ComputerAided Design
, 1996
"... This paper discusses the analysis of large linear electrical networks consisting of passive components, such as resistors, capacitors, inductors, and transformers. Such networks admit a symmetric formulation of their circuit equations. We introduce SyPVL, an eficient and numerically stable algorit ..."
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Cited by 42 (14 self)
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This paper discusses the analysis of large linear electrical networks consisting of passive components, such as resistors, capacitors, inductors, and transformers. Such networks admit a symmetric formulation of their circuit equations. We introduce SyPVL, an eficient and numerically stable algorithm for the computation of reducedorder models of large, linear, passive networks. SyPVL represents the specialization of the more general PVL algorithm, to symmetric problems. Besides the gain in eficiency over PVL, SyPVL also preserves the symmetry of the problem, and, as a consequence, can often guarantee the stability of the resulting reducedorder models. Moreover, these reducedorder models can be synthesized as actual physical circuits, thus facilitating compatibility with existing analysis tools. The application of SyPVL is illustrated with two interconnectanalysis examples. 1
Model Reduction Methods Based on Krylov Subspaces
 Acta Numerica
, 2003
"... This paper reviews the main ideas of reducedorder modeling techniques based on Krylov subspaces and describes some applications of reducedorder modeling in circuit simulation ..."
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Cited by 37 (6 self)
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This paper reviews the main ideas of reducedorder modeling techniques based on Krylov subspaces and describes some applications of reducedorder modeling in circuit simulation
Efficient Frequency Domain Analysis of Large Nonlinear Analog Circuits
, 1996
"... In this paper, we present a new implementation of the harmonic balance method which extends its applicability to circuits 23 orders of magnitude larger than was previously practical. The results reported here extend our previous work [1] which only considered large circuits operating in a mildly no ..."
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Cited by 25 (2 self)
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In this paper, we present a new implementation of the harmonic balance method which extends its applicability to circuits 23 orders of magnitude larger than was previously practical. The results reported here extend our previous work [1] which only considered large circuits operating in a mildly nonlinear regime. The new implementation is based on quadratically convergent Newton methods and is able to simulate general nonlinear circuits. The significant efficiency improvement is achieved by use of Krylov subspace methods and a problemspecific preconditioner for inverting the harmonic balance Jacobian matrix. The analysis of radiofrequency mixers, implemented in integrated circuit technology, is an important application of our new method. We describe the theory behind the method, then report performance results on a complete receiver design using detailed transistor models. I. Introduction The method of Harmonic Balance is well established for fast and accurate steadystate analysi...
Simulation and optimization of the power distribution network
 in VLSI circuits,” in Proc. Int. Conf. Comput.Aided Des
"... In this paper, we present simulation techniques to estimate the worstcase voltage variation using a RC model for the power distribution network. Pattern independent maximum envelope currents are used as a periodic input for performing the frequencydomain steadystate simulation of the linear RC ci ..."
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Cited by 20 (0 self)
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In this paper, we present simulation techniques to estimate the worstcase voltage variation using a RC model for the power distribution network. Pattern independent maximum envelope currents are used as a periodic input for performing the frequencydomain steadystate simulation of the linear RC circuit to evaluate the worstcase instantaneous voltage drop for the RC power distribution networks. The proposed technique unlike existing techniques, is guaranteed to give the maximum voltage drop at nodes in the RC power distribution network. We present experimental results to compare the frequencydomain and timedomain simulation techniques for estimating the maximum instantaneous voltage drop. We also present frequency domain sensitivity analysis based decoupling capacitance placement for reducing the voltage variation in the power distribution network. Experimental results on circuits extracted from layout are presented to validate the simulation and optimization techniques. 1
Passive ReducedOrder Models for Interconnect Simulation and their Computation via KrylovSubspace Algorithms
 In Proc. 36th ACM/IEEE Design Automation Conference
, 1998
"... This paper studies a general projection technique based on block Krylov subspaces for the computation of reducedorder models of multiport RLC circuits. We show that the resulting reducedorder models are always passive, yet they still match at least half as many moments as the corresponding reduce ..."
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Cited by 19 (9 self)
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This paper studies a general projection technique based on block Krylov subspaces for the computation of reducedorder models of multiport RLC circuits. We show that the resulting reducedorder models are always passive, yet they still match at least half as many moments as the corresponding reducedorder models based on matrixPad 'e approximation. Moreover, for the special cases of RC, RL, and LC circuits, the reducedorder models obtained by projection and by matrixPad'e approximation are identical. For general RLC circuits, we show how the projection technique can easily be incorporated into the SyMPVL algorithm to obtain passive reducedorder models, in addition to the highaccuracy matrixPad'e approximation that characterizes SyMPVL, at essentially no extra computational costs. Connections between SyMPVL and the recently proposed reducedorder modeling algorithm PRIMA are also discussed. Numerical results for interconnect simulation problems are reported. 1 Introduction Electr...